Non-Linear Hydromagnetic Waves Propagating along a Magnetic Field in a Cold Collision-Free Plasma

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Non-linear hydromagnetic waves propagating along a uniform magnetic field in a cold collision-free plasma are dealt with. It is assumed that the plasma is fully ionized and quasi-neutral, and that the loop-motion of the plasma particles does not occur.
The solutions of the problem are divided into two classes according as l is equal to zero or not, where l is a parameter relating to the angular momentum flux carried by the plasma particles in the direction of the uniform magnetic field. In both cases, exact solutions representing wave-trains can be obtained in terms of Jacobian elliptic functions. In particular, the first class (l=0) includes an isolated pulse solution as a special case.